## Debussche, Arnaud

Compute Distance To:
 Author ID: debussche.arnaud Published as: Debussche, Arnaud; Debussche, A.
 Documents Indexed: 115 Publications since 1990, including 1 Book 1 Contribution as Editor · 1 Further Contribution Co-Authors: 58 Co-Authors with 108 Joint Publications 1,460 Co-Co-Authors
all top 5

### Co-Authors

 8 single-authored 25 Da Prato, Giuseppe 20 de Bouard, Anne 10 Temam, Roger Meyer 9 Vovelle, Julien 5 Di Menza, Laurent 4 Printems, Jacques 4 Tsutsumi, Yoshio 3 De Moor, Sylvain 3 Hofmanová, Martina 3 Tubaro, Luciano 2 Alouges, François 2 Barbu, Viorel 2 Cerrai, Sandra 2 Dubois, Thierry 2 Faou, Erwan 2 Flandoli, Franco 2 Fukuizumi, Reika 2 Glatt-Holtz, Nathan E. 2 Högele, Michael Anton 2 Imkeller, Peter 2 Laminie, Jacques 2 Odasso, Cyril 2 Radulescu, Ovidiu 2 Tessitore, Gianmario 1 Albeverio, Sergio A. 1 Antoneli, Fernando jun. 1 Bailleul, Ismaël F. 1 Barton-Smith, Marc 1 Beirão da Veiga, Hugo 1 Belaouar, Radoin 1 Bréhier, Charles-Edouard 1 Calgaro, Caterina 1 Charrier, Julia 1 Chernov, Alexey 1 Constantin, Peter 1 Cortes, Julien 1 Crauel, Hans 1 Crudu, A. 1 de Bernard, Anne 1 Dettori, Lucia 1 Fournier, Nicolas G. 1 Fuhrman, Marco 1 Galdi, Giovanni Paolo 1 Gautier, Eric 1 Goldys, Beniamin 1 Goudenège, Ludovic 1 Hodgkinson, Arran 1 Hu, Ying 1 Innocentini, Guilherme C. P. 1 Martin, Jörg 1 Nguepedja Nankep, Mac Jugal 1 Nobile, Fabio 1 Poncet, Romain 1 Romito, Marco 1 Rosello, Angelo 1 Růžička, Michael 1 Seregin, Gregory A. 1 Toumi, I. 1 Weber, Hendrik 1 Xu, Lihu 1 Zahrouni, Ezzeddine 1 Zambotti, Lorenzo 1 Ziane, Mohammed
all top 5

### Serials

 7 Journal of Functional Analysis 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 The Annals of Probability 4 Applied Mathematics and Optimization 4 Physica D 4 Probability Theory and Related Fields 4 Applied Mathematics Letters 4 SIAM Journal on Mathematical Analysis 4 Stochastic and Partial Differential Equations. Analysis and Computations 3 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 3 Differential and Integral Equations 3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 3 Electronic Communications in Probability 3 Journal of Evolution Equations 2 Nonlinearity 2 Mathematics of Computation 2 Numerische Mathematik 2 SIAM Journal on Numerical Analysis 2 Stochastic Analysis and Applications 2 Asymptotic Analysis 2 The Annals of Applied Probability 2 Stochastic Processes and their Applications 2 Journal of Dynamics and Differential Equations 2 Séminaire Équations aux Dérivées Partielles 2 Electronic Journal of Probability 2 Discrete and Continuous Dynamical Systems 2 Lecture Notes in Mathematics 2 Nonlinear Analysis. Theory, Methods & Applications 1 Communications in Mathematical Physics 1 International Journal for Numerical Methods in Fluids 1 Journal of Computational Physics 1 Journal of Statistical Physics 1 Theoretical and Computational Fluid Dynamics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Journal of Differential Equations 1 Numerical Functional Analysis and Optimization 1 SIAM Journal on Control and Optimization 1 Theoretical Computer Science 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Numerical Methods for Partial Differential Equations 1 Journal of Scientific Computing 1 Stochastics and Stochastics Reports 1 Potential Analysis 1 NoDEA. Nonlinear Differential Equations and Applications 1 Monte Carlo Methods and Applications 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 Journal of Computational Analysis and Applications 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 Communications on Pure and Applied Analysis 1 Discrete and Continuous Dynamical Systems. Series S 1 Kinetic and Related Models 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Tunisian Journal of Mathematics
all top 5

### Fields

 94 Partial differential equations (35-XX) 78 Probability theory and stochastic processes (60-XX) 24 Fluid mechanics (76-XX) 19 Numerical analysis (65-XX) 16 Dynamical systems and ergodic theory (37-XX) 8 Ordinary differential equations (34-XX) 5 Quantum theory (81-XX) 4 Operator theory (47-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Systems theory; control (93-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Biology and other natural sciences (92-XX) 2 General and overarching topics; collections (00-XX) 2 Measure and integration (28-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Astronomy and astrophysics (85-XX) 2 Geophysics (86-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Differential geometry (53-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Operations research, mathematical programming (90-XX)

### Citations contained in zbMATH Open

106 Publications have been cited 2,672 times in 1,744 Documents Cited by Year
Random attractors. Zbl 0884.58064
Crauel, Hans; Debussche, Arnaud; Flandoli, Franco
1997
Stochastic Burgers’ equation. Zbl 0824.35112
Da Prato, Giuseppe; Debussche, Arnaud; Temam, Roger
1994
Strong solutions to the stochastic quantization equations. Zbl 1071.81070
Da Prato, Giuseppe; Debussche, Arnaud
2003
Two-dimensional Navier-Stokes equations driven by a space-time white noise. Zbl 1013.60051
Da Prato, Giuseppe; Debussche, Arnaud
2002
The stochastic nonlinear Schrödinger equation in $$H^1$$. Zbl 1027.60065
de Bouard, A.; Debussche, A.
2003
Ergodicity for the 3D stochastic Navier-Stokes equations. Zbl 1109.60047
Da Prato, Giuseppe; Debussche, Arnaud
2003
Stochastic Cahn-Hilliard equation. Zbl 0838.60056
Da Prato, Giuseppe; Debussche, Arnaud
1996
Scalar conservation laws with stochastic forcing. Zbl 1200.60050
Debussche, A.; Vovelle, J.
2010
A stochastic nonlinear Schrödinger equation with multiplicative noise. Zbl 0952.60061
de Bouard, A.; Debussche, A.
1999
On the Cahn-Hilliard equation with a logarithmic free energy. Zbl 0831.35088
Debussche, Arnaud; Dettori, Lucia
1995
Local martingale and pathwise solutions for an abstract fluids model. Zbl 1230.60065
Debussche, Arnaud; Glatt-Holtz, Nathan; Temam, Roger
2011
Hausdorff dimension of a random invariant set. Zbl 0919.58044
Debussche, A.
1998
On the stochastic Korteweg-de Vries equation. Zbl 0912.60074
de Bouard, A.; Debussche, A.
1998
Weak order for the discretization of the stochastic heat equation. Zbl 1215.60043
Debussche, Arnaud; Printems, Jacques
2009
Degenerate parabolic stochastic partial differential equations: quasilinear case. Zbl 1346.60094
Debussche, Arnaud; Hofmanová, Martina; Vovelle, Julien
2016
On the finite dimensionality of random attractors. Zbl 0888.60051
Debussche, A.
1997
Weak approximation of stochastic partial differential equations: the nonlinear case. Zbl 1217.65011
Debussche, Arnaud
2011
Convergence of stochastic gene networks to hybrid piecewise deterministic processes. Zbl 1261.60073
Crudu, A.; Debussche, A.; Muller, A.; Radulescu, O.
2012
White noise driven Korteweg-de Vries equation. Zbl 0952.60062
de Bouard, A.; Debussche, A.; Tsutsumi, Y.
1999
Weak and strong order of convergence of a semidiscrete scheme for the stochastic nonlinear Schrödinger equation. Zbl 1109.60051
de Bouard, Anne; Debussche, Arnaud
2006
Numerical simulation of the stochastic Korteweg-de Vries equation. Zbl 0948.76038
Debussche, Arnaud; Printems, Jacques
1999
Blowup for the stochastic nonlinear Schrödinger equation with multiplicative noise. Zbl 1068.35191
de Bouard, Anne; Debussche, Arnaud
2005
Numerical simulation of focusing stochastic nonlinear Schrödinger equations. Zbl 0988.35156
Debussche, Arnaud; Di Menza, Laurent
2002
Markov solutions for the 3D stochastic Navier-Stokes equations with state dependent noise. Zbl 1110.35110
Debussche, Arnaud; Odasso, Cyril
2006
On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation. Zbl 1008.35074
de Bouard, A.; Debussche, A.
2002
Ergodicity results for the stochastic Navier-Stokes equations: an introduction. Zbl 1301.35086
Debussche, Arnaud
2013
Existence of densities for stable-like driven SDEs with Hölder continuous coefficients. Zbl 1272.60032
Debussche, Arnaud; Fournier, Nicolas
2013
A semi-discrete scheme for the stochastic nonlinear Schrödinger equation. Zbl 1055.65008
de Bouard, A.; Debussche, A.
2004
Conservative stochastic Cahn-Hilliard equation with reflection. Zbl 1130.60068
Debussche, Arnaud; Zambotti, Lorenzo
2007
Global existence and regularity for the 3D stochastic primitive equations of the ocean and atmosphere with multiplicative white noise. Zbl 1246.35194
Debussche, A.; Glatt-Holtz, N.; Temam, R.; Ziane, M.
2012
1D quintic nonlinear Schrödinger equation with white noise dispersion. Zbl 1234.35242
Debussche, Arnaud; Tsutsumi, Yoshio
2011
Optimal control of a stochastic heat equation with boundary-noise and boundary-control. Zbl 1123.60052
Debussche, Arnaud; Fuhrman, Marco; Tessitore, Gianmario
2007
The nonlinear Schrödinger equation with white noise dispersion. Zbl 1193.35213
de Bouard, Anne; Debussche, Arnaud
2010
A regularity result for quasilinear stochastic partial differential equations of parabolic type. Zbl 1327.60124
Debussche, Arnaud; de Moor, Sylvain; Hofmanová, Martina
2015
The nonlinear Galerkin method: A multiscale method applied to the simulation of homogeneous turbulent flows. Zbl 0838.76060
Debussche, A.; Dubois, T.; Temam, Roger
1995
Invariant measure of scalar first-order conservation laws with stochastic forcing. Zbl 1331.60117
Debussche, A.; Vovelle, J.
2015
A density perturbation method to study the eigenstructure of two-phase flow equation systems. Zbl 0917.76047
Cortes, Julien; Debussche, A.; Toumi, I.
1998
On the construction of families of approximate inertial manifolds. Zbl 0760.34050
Debussche, A.; Marion, M.
1992
Ergodic BSDEs under weak dissipative assumptions. Zbl 1221.60080
Debussche, Arnaud; Hu, Ying; Tessitore, Gianmario
2011
Ergodicity for a weakly damped stochastic nonlinear Schrödinger equation. Zbl 1091.60010
Debussche, Arnaud; Odasso, Cyril
2005
Some properties of invariant measures of non symmetric dissipative stochastic systems. Zbl 1087.60049
Da Prato, Giuseppe; Debussche, Arnaud; Goldys, Beniamin
2002
Stochastic Cahn-Hilliard equation with double singular nonlinearities and two reflections. Zbl 1233.60036
Debussche, Arnaud; Goudenège, Ludovic
2011
Construction of stochastic inertial manifolds using backward integration. Zbl 0876.60040
Da Prato, Giuseppe; Debussche, Arnaud
1996
Weak backward error analysis for SDEs. Zbl 1256.65002
Debussche, Arnaud; Faou, Erwan
2012
$$m$$-dissipativity of Kolmogorov operators corresponding to Burgers equations with space-time white noise. Zbl 1119.35128
Da Prato, Giuseppe; Debussche, Arnaud
2007
Modified energy for split-step methods applied to the linear Schrödinger equation. Zbl 1209.65137
Debussche, Arnaud; Faou, Erwan
2009
Existence of densities for the 3D Navier-Stokes equations driven by Gaussian noise. Zbl 1452.76193
Debussche, Arnaud; Romito, Marco
2014
Some new generalizations of inertial manifolds. Zbl 0948.35018
Debussche, A.; Temam, R.
1996
Convergent families of approximate inertial manifolds. Zbl 0836.35063
Debussche, A.; Temam, R.
1994
The dynamics of nonlinear reaction-diffusion equations with small Lévy noise. Zbl 1321.60004
Debussche, Arnaud; Högele, Michael; Imkeller, Peter
2013
Periodic solutions of the Korteweg–de Vries equation driven by white noise. Zbl 1075.35121
De Bouard, A.; Debussche, A.; Tsutsumi, Y.
2004
A singular perturbation of the Cahn-Hilliard equation. Zbl 0741.35023
Debussche, Arnaud
1991
On the qualitative behaviour of the orbits of a parabolic partial differential equation and its discretization in the neighborhood of a hyperbolic fixed point. Zbl 0770.35027
Alouges, François; Debussche, Arnaud
1991
Weak truncation error estimates for elliptic PDEs with lognormal coefficients. Zbl 1273.65166
Charrier, Julia; Debussche, Arnaud
2013
Control of the stochastic Burgers model of turbulence. Zbl 1111.49302
Da Prato, Giuseppe; Debussche, Arnaud
1999
2D stochastic Navier-Stokes equations with a time-periodic forcing term. Zbl 1154.35099
Da Prato, Giuseppe; Debussche, Arnaud
2008
Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient. Zbl 1428.60089
Bréhier, Charles-Edouard; Debussche, Arnaud
2018
Dynamic programming for the stochastic Navier-Stokes equations. Zbl 0953.76016
da Prato, Giuseppe; Debussche, Arnaud
2000
Numerical study of two-dimensional stochastic NLS equations. Zbl 1077.65006
Barton-Smith, Marc; Debussche, Arnaud; Di Menza, Laurent
2005
Inertial manifolds and the slow manifolds in meteorology. Zbl 0753.35043
Debussche, A.; Temam, R.
1991
Numerical analysis of the nonlinear Schrödinger equation with white noise dispersion. Zbl 1314.35159
Belaouar, Radoin; de Bouard, Anne; Debussche, Arnaud
2015
Differentiability of the transition semigroup of the stochastic Burgers equations, and application to the corresponding Hamilton-Jacobi equation. Zbl 0931.37036
Da Prato, Giuseppe; Debussche, Arnaud
1998
Diffusion limit for a stochastic kinetic problem. Zbl 1267.35022
Debussche, Arnaud; Vovelle, Julien
2012
Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises. Zbl 1303.60051
Albeverio, Sergio; Debussche, Arnaud; Xu, Lihu
2012
The Korteweg-de Vries equation with multiplicative homogeneous noise. Zbl 1137.35086
de Bouard, Anne; Debussche, Arnaud
2007
Small noise asymptotic of the timing jitter in soliton transmission. Zbl 1147.60041
Debussche, Arnaud; Gautier, Eric
2008
The Kolmogorov equation associated to the stochastic Navier-Stokes equations in 2D. Zbl 1085.60041
Barbu, Viorel; Da Prato, Giuseppe; Debussche, Arnaud
2004
Convergence of a semi-discrete scheme for the stochastic Korteweg-de Vries equation. Zbl 1132.35076
Debussche, Arnaud; Printems, Jacques
2006
Quasilinear generalized parabolic Anderson model equation. Zbl 1448.35320
Bailleul, I.; Debussche, A.; Hofmanová, M.
2019
The Schrödinger equation with spatial white noise potential. Zbl 1387.60097
Debussche, Arnaud; Weber, Hendrik
2018
Essential $$m$$-dissipativity of Kolmogorov operators corresponding to periodic 2D-Navier Stokes equations. Zbl 1096.35126
Da Prato, Giuseppe; Barbu, Viorel; Debussche, Arnaud
2004
A modified Kardar-Parisi-Zhang model. Zbl 1136.60043
Da Prato, Giuseppe; Debussche, Arnaud; Tubaro, Luciano
2007
Random modulation of solitons for the stochastic Korteweg-de Vries equation. Zbl 1158.60359
de Bouard, A.; Debussche, A.
2007
An integral inequality for the invariant measure of a stochastic reaction-diffusion equation. Zbl 1364.60080
Da Prato, Giuseppe; Debussche, Arnaud
2017
The 2D-Navier-Stokes equations perturbed by a delta correlated noise. Zbl 1067.76023
Debussche, A.
2003
Inertial manifolds and slow manifolds. Zbl 0723.58006
Debussche, A.; Temam, R.
1991
Dynamic programming for the stochastic Burgers equation. Zbl 1016.49024
Da Prato, Giuseppe; Debussche, Arnaud
2000
Effect of a localized random forcing term on the Korteweg-de Vries equation. Zbl 1032.35155
Debussche, Arnaud; Printems, Jacques
2001
On a multilevel approach for the two-dimensional Navier-Stokes equations with finite elements. Zbl 0914.76049
Calgaro, C.; Debussche, A.; Laminie, J.
1998
Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn-Hilliard equation. Zbl 1038.60055
Da Prato, Giuseppe; Debussche, Arnaud; Tubaro, Luciano
2004
On the martingale problem associated to the 2D and 3D stochastic Navier-Stokes equations. Zbl 1194.76033
Da Prato, Giuseppe; Debussche, Arnaud
2008
Large deviations for the two-dimensional stochastic Navier-Stokes equation with vanishing noise correlation. Zbl 1418.60069
Cerrai, Sandra; Debussche, Arnaud
2019
Estimate for $$P_{t}D$$ for the stochastic Burgers equation. Zbl 1350.60057
Da Prato, Giuseppe; Debussche, Arnaud
2016
On the discretization of a partial differential equation in the neighborhood of a periodic orbit. Zbl 0791.65071
Alouges, François; Debussche, Arnaud
1993
Approximation of exponential order of the attractor of a turbulent flow. Zbl 0814.76030
Debussche, A.; Dubois, T.
1994
Numerical resolution of stochastic focusing NLS equations. Zbl 1001.65006
Debussche, A.; Di Menza, L.
2002
A dynamical multi-level scheme for the Burgers equation: Wavelet and hierarchical finite element. Zbl 1087.76063
Debussche, A.; Laminie, J.; Zahrouni, E.
2005
Absolute continuity of the invariant measures for some stochastic PDEs. Zbl 1157.60333
Da Prato, Giuseppe; Debussche, Arnaud
2004
Solution to the stochastic Schrödinger equation on the full space. Zbl 1407.35236
Debussche, Arnaud; Martin, Jörg
2019
Diffusion-approximation in stochastically forced kinetic equations. Zbl 1442.35286
Debussche, Arnaud; Vovelle, Julien
2021
Coupling for some partial differential equations driven by white noise. Zbl 1079.60061
Da Prato, Giuseppe; Debussche, Arnaud; Tubaro, Luciano
2005
Inertial manifolds with delay. Zbl 0822.34041
Debussche, A.; Temam, R.
1995
Diffusion limit for the radiative transfer equation perturbed by a Markovian process. Zbl 1344.35148
Debussche, A.; De Moor, S.; Vovelle, J.
2016
Long-time behavior in scalar conservation laws. Zbl 1240.35352
Debussche, A.; Vovelle, J.
2009
Asymptotic first exit times of the Chafee-Infante equation with small heavy-tailed Lévy noise. Zbl 1233.60037
Debussche, Arnaud; Hoegele, Michael; Imkeller, Peter
2011
Maximal dissipativity of the Dirichlet operator corresponding to the Burgers equation. Zbl 0978.60069
Da Prato, Giuseppe; Debussche, Arnaud
2000
Inertial manifolds and Sacker’s equation. Zbl 0731.58057
Debussche, Arnaud
1990
Quasi-invariance of Gaussian measures transported by the cubic NLS with third-order dispersion on T. Zbl 1464.35317
Debussche, Arnaud; Tsutsumi, Yoshio
2021
A convergent family of approximate inertial manifolds. Zbl 0769.34047
Debussche, A.; Temam, R.
1993
Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise. Zbl 1185.35222
de Bouard, Anne; Debussche, Arnaud
2009
Diffusion-approximation in stochastically forced kinetic equations. Zbl 1442.35286
Debussche, Arnaud; Vovelle, Julien
2021
Quasi-invariance of Gaussian measures transported by the cubic NLS with third-order dispersion on T. Zbl 1464.35317
Debussche, Arnaud; Tsutsumi, Yoshio
2021
Quasilinear generalized parabolic Anderson model equation. Zbl 1448.35320
Bailleul, I.; Debussche, A.; Hofmanová, M.
2019
Large deviations for the two-dimensional stochastic Navier-Stokes equation with vanishing noise correlation. Zbl 1418.60069
Cerrai, Sandra; Debussche, Arnaud
2019
Solution to the stochastic Schrödinger equation on the full space. Zbl 1407.35236
Debussche, Arnaud; Martin, Jörg
2019
Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient. Zbl 1428.60089
Bréhier, Charles-Edouard; Debussche, Arnaud
2018
The Schrödinger equation with spatial white noise potential. Zbl 1387.60097
Debussche, Arnaud; Weber, Hendrik
2018
Long time behavior of Gross-Pitaevskii equation at positive temperature. Zbl 1406.35376
de Bouard, Anne; Debussche, Arnaud; Fukuizumi, Reika
2018
An integral inequality for the invariant measure of a stochastic reaction-diffusion equation. Zbl 1364.60080
Da Prato, Giuseppe; Debussche, Arnaud
2017
Degenerate parabolic stochastic partial differential equations: quasilinear case. Zbl 1346.60094
Debussche, Arnaud; Hofmanová, Martina; Vovelle, Julien
2016
Estimate for $$P_{t}D$$ for the stochastic Burgers equation. Zbl 1350.60057
Da Prato, Giuseppe; Debussche, Arnaud
2016
Diffusion limit for the radiative transfer equation perturbed by a Markovian process. Zbl 1344.35148
Debussche, A.; De Moor, S.; Vovelle, J.
2016
A regularity result for quasilinear stochastic partial differential equations of parabolic type. Zbl 1327.60124
Debussche, Arnaud; de Moor, Sylvain; Hofmanová, Martina
2015
Invariant measure of scalar first-order conservation laws with stochastic forcing. Zbl 1331.60117
Debussche, A.; Vovelle, J.
2015
Numerical analysis of the nonlinear Schrödinger equation with white noise dispersion. Zbl 1314.35159
Belaouar, Radoin; de Bouard, Anne; Debussche, Arnaud
2015
Diffusion limit for the radiative transfer equation perturbed by a Wiener process. Zbl 1333.35295
Debussche, Arnaud; De Moor, Sylvain; Vovelle, Julien
2015
Existence of densities for the 3D Navier-Stokes equations driven by Gaussian noise. Zbl 1452.76193
Debussche, Arnaud; Romito, Marco
2014
Ergodicity results for the stochastic Navier-Stokes equations: an introduction. Zbl 1301.35086
Debussche, Arnaud
2013
Existence of densities for stable-like driven SDEs with Hölder continuous coefficients. Zbl 1272.60032
Debussche, Arnaud; Fournier, Nicolas
2013
The dynamics of nonlinear reaction-diffusion equations with small Lévy noise. Zbl 1321.60004
Debussche, Arnaud; Högele, Michael; Imkeller, Peter
2013
Weak truncation error estimates for elliptic PDEs with lognormal coefficients. Zbl 1273.65166
Charrier, Julia; Debussche, Arnaud
2013
Convergence of stochastic gene networks to hybrid piecewise deterministic processes. Zbl 1261.60073
Crudu, A.; Debussche, A.; Muller, A.; Radulescu, O.
2012
Global existence and regularity for the 3D stochastic primitive equations of the ocean and atmosphere with multiplicative white noise. Zbl 1246.35194
Debussche, A.; Glatt-Holtz, N.; Temam, R.; Ziane, M.
2012
Weak backward error analysis for SDEs. Zbl 1256.65002
Debussche, Arnaud; Faou, Erwan
2012
Diffusion limit for a stochastic kinetic problem. Zbl 1267.35022
Debussche, Arnaud; Vovelle, Julien
2012
Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises. Zbl 1303.60051
Albeverio, Sergio; Debussche, Arnaud; Xu, Lihu
2012
Local martingale and pathwise solutions for an abstract fluids model. Zbl 1230.60065
Debussche, Arnaud; Glatt-Holtz, Nathan; Temam, Roger
2011
Weak approximation of stochastic partial differential equations: the nonlinear case. Zbl 1217.65011
Debussche, Arnaud
2011
1D quintic nonlinear Schrödinger equation with white noise dispersion. Zbl 1234.35242
Debussche, Arnaud; Tsutsumi, Yoshio
2011
Ergodic BSDEs under weak dissipative assumptions. Zbl 1221.60080
Debussche, Arnaud; Hu, Ying; Tessitore, Gianmario
2011
Stochastic Cahn-Hilliard equation with double singular nonlinearities and two reflections. Zbl 1233.60036
Debussche, Arnaud; Goudenège, Ludovic
2011
Asymptotic first exit times of the Chafee-Infante equation with small heavy-tailed Lévy noise. Zbl 1233.60037
Debussche, Arnaud; Hoegele, Michael; Imkeller, Peter
2011
Scalar conservation laws with stochastic forcing. Zbl 1200.60050
Debussche, A.; Vovelle, J.
2010
The nonlinear Schrödinger equation with white noise dispersion. Zbl 1193.35213
de Bouard, Anne; Debussche, Arnaud
2010
Asymptotic behavior of stochastic PDEs with random coefficients. Zbl 1213.37122
da Prato, Giuseppe; Debussche, Arnaud
2010
Weak order for the discretization of the stochastic heat equation. Zbl 1215.60043
Debussche, Arnaud; Printems, Jacques
2009
Modified energy for split-step methods applied to the linear Schrödinger equation. Zbl 1209.65137
Debussche, Arnaud; Faou, Erwan
2009
Long-time behavior in scalar conservation laws. Zbl 1240.35352
Debussche, A.; Vovelle, J.
2009
Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise. Zbl 1185.35222
de Bouard, Anne; Debussche, Arnaud
2009
2D stochastic Navier-Stokes equations with a time-periodic forcing term. Zbl 1154.35099
Da Prato, Giuseppe; Debussche, Arnaud
2008
Small noise asymptotic of the timing jitter in soliton transmission. Zbl 1147.60041
Debussche, Arnaud; Gautier, Eric
2008
On the martingale problem associated to the 2D and 3D stochastic Navier-Stokes equations. Zbl 1194.76033
Da Prato, Giuseppe; Debussche, Arnaud
2008
On a stochastic Korteweg-de Vries equation with homogeneous noise. Zbl 1176.35165
de Bernard, Anne; Debussche, Arnaud
2008
Conservative stochastic Cahn-Hilliard equation with reflection. Zbl 1130.60068
Debussche, Arnaud; Zambotti, Lorenzo
2007
Optimal control of a stochastic heat equation with boundary-noise and boundary-control. Zbl 1123.60052
Debussche, Arnaud; Fuhrman, Marco; Tessitore, Gianmario
2007
$$m$$-dissipativity of Kolmogorov operators corresponding to Burgers equations with space-time white noise. Zbl 1119.35128
Da Prato, Giuseppe; Debussche, Arnaud
2007
The Korteweg-de Vries equation with multiplicative homogeneous noise. Zbl 1137.35086
de Bouard, Anne; Debussche, Arnaud
2007
A modified Kardar-Parisi-Zhang model. Zbl 1136.60043
Da Prato, Giuseppe; Debussche, Arnaud; Tubaro, Luciano
2007
Random modulation of solitons for the stochastic Korteweg-de Vries equation. Zbl 1158.60359
de Bouard, A.; Debussche, A.
2007
Weak and strong order of convergence of a semidiscrete scheme for the stochastic nonlinear Schrödinger equation. Zbl 1109.60051
de Bouard, Anne; Debussche, Arnaud
2006
Markov solutions for the 3D stochastic Navier-Stokes equations with state dependent noise. Zbl 1110.35110
Debussche, Arnaud; Odasso, Cyril
2006
Convergence of a semi-discrete scheme for the stochastic Korteweg-de Vries equation. Zbl 1132.35076
Debussche, Arnaud; Printems, Jacques
2006
Blowup for the stochastic nonlinear Schrödinger equation with multiplicative noise. Zbl 1068.35191
de Bouard, Anne; Debussche, Arnaud
2005
Ergodicity for a weakly damped stochastic nonlinear Schrödinger equation. Zbl 1091.60010
Debussche, Arnaud; Odasso, Cyril
2005
Numerical study of two-dimensional stochastic NLS equations. Zbl 1077.65006
Barton-Smith, Marc; Debussche, Arnaud; Di Menza, Laurent
2005
A dynamical multi-level scheme for the Burgers equation: Wavelet and hierarchical finite element. Zbl 1087.76063
Debussche, A.; Laminie, J.; Zahrouni, E.
2005
Coupling for some partial differential equations driven by white noise. Zbl 1079.60061
Da Prato, Giuseppe; Debussche, Arnaud; Tubaro, Luciano
2005
A semi-discrete scheme for the stochastic nonlinear Schrödinger equation. Zbl 1055.65008
de Bouard, A.; Debussche, A.
2004
Periodic solutions of the Korteweg–de Vries equation driven by white noise. Zbl 1075.35121
De Bouard, A.; Debussche, A.; Tsutsumi, Y.
2004
The Kolmogorov equation associated to the stochastic Navier-Stokes equations in 2D. Zbl 1085.60041
Barbu, Viorel; Da Prato, Giuseppe; Debussche, Arnaud
2004
Essential $$m$$-dissipativity of Kolmogorov operators corresponding to periodic 2D-Navier Stokes equations. Zbl 1096.35126
Da Prato, Giuseppe; Barbu, Viorel; Debussche, Arnaud
2004
Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn-Hilliard equation. Zbl 1038.60055
Da Prato, Giuseppe; Debussche, Arnaud; Tubaro, Luciano
2004
Absolute continuity of the invariant measures for some stochastic PDEs. Zbl 1157.60333
Da Prato, Giuseppe; Debussche, Arnaud
2004
Strong solutions to the stochastic quantization equations. Zbl 1071.81070
Da Prato, Giuseppe; Debussche, Arnaud
2003
The stochastic nonlinear Schrödinger equation in $$H^1$$. Zbl 1027.60065
de Bouard, A.; Debussche, A.
2003
Ergodicity for the 3D stochastic Navier-Stokes equations. Zbl 1109.60047
Da Prato, Giuseppe; Debussche, Arnaud
2003
The 2D-Navier-Stokes equations perturbed by a delta correlated noise. Zbl 1067.76023
Debussche, A.
2003
Two-dimensional Navier-Stokes equations driven by a space-time white noise. Zbl 1013.60051
Da Prato, Giuseppe; Debussche, Arnaud
2002
Numerical simulation of focusing stochastic nonlinear Schrödinger equations. Zbl 0988.35156
Debussche, Arnaud; Di Menza, Laurent
2002
On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation. Zbl 1008.35074
de Bouard, A.; Debussche, A.
2002
Some properties of invariant measures of non symmetric dissipative stochastic systems. Zbl 1087.60049
Da Prato, Giuseppe; Debussche, Arnaud; Goldys, Beniamin
2002
Numerical resolution of stochastic focusing NLS equations. Zbl 1001.65006
Debussche, A.; Di Menza, L.
2002
Finite-time blow-up in the additive supercritical stochastic nonlinear Schrödinger equation: The real noise case. Zbl 1017.35105
de Bouard, A.; Debussche, A.
2002
Effect of a localized random forcing term on the Korteweg-de Vries equation. Zbl 1032.35155
Debussche, Arnaud; Printems, Jacques
2001
Theoretical and numerical aspects of stochastic nonlinear Schrödinger equations. Zbl 0989.65002
de Bouard, A.; Debussche, A.; Di Menza, L.
2001
Dynamic programming for the stochastic Navier-Stokes equations. Zbl 0953.76016
da Prato, Giuseppe; Debussche, Arnaud
2000
Dynamic programming for the stochastic Burgers equation. Zbl 1016.49024
Da Prato, Giuseppe; Debussche, Arnaud
2000
Maximal dissipativity of the Dirichlet operator corresponding to the Burgers equation. Zbl 0978.60069
Da Prato, Giuseppe; Debussche, Arnaud
2000
A stochastic nonlinear Schrödinger equation with multiplicative noise. Zbl 0952.60061
de Bouard, A.; Debussche, A.
1999
White noise driven Korteweg-de Vries equation. Zbl 0952.60062
de Bouard, A.; Debussche, A.; Tsutsumi, Y.
1999
Numerical simulation of the stochastic Korteweg-de Vries equation. Zbl 0948.76038
Debussche, Arnaud; Printems, Jacques
1999
Control of the stochastic Burgers model of turbulence. Zbl 1111.49302
Da Prato, Giuseppe; Debussche, Arnaud
1999
Hausdorff dimension of a random invariant set. Zbl 0919.58044
Debussche, A.
1998
On the stochastic Korteweg-de Vries equation. Zbl 0912.60074
de Bouard, A.; Debussche, A.
1998
A density perturbation method to study the eigenstructure of two-phase flow equation systems. Zbl 0917.76047
Cortes, Julien; Debussche, A.; Toumi, I.
1998
Differentiability of the transition semigroup of the stochastic Burgers equations, and application to the corresponding Hamilton-Jacobi equation. Zbl 0931.37036
Da Prato, Giuseppe; Debussche, Arnaud
1998
On a multilevel approach for the two-dimensional Navier-Stokes equations with finite elements. Zbl 0914.76049
Calgaro, C.; Debussche, A.; Laminie, J.
1998
Random attractors. Zbl 0884.58064
Crauel, Hans; Debussche, Arnaud; Flandoli, Franco
1997
On the finite dimensionality of random attractors. Zbl 0888.60051
Debussche, A.
1997
Stochastic Cahn-Hilliard equation. Zbl 0838.60056
Da Prato, Giuseppe; Debussche, Arnaud
1996
Construction of stochastic inertial manifolds using backward integration. Zbl 0876.60040
Da Prato, Giuseppe; Debussche, Arnaud
1996
Some new generalizations of inertial manifolds. Zbl 0948.35018
Debussche, A.; Temam, R.
1996
On the Cahn-Hilliard equation with a logarithmic free energy. Zbl 0831.35088
Debussche, Arnaud; Dettori, Lucia
1995
The nonlinear Galerkin method: A multiscale method applied to the simulation of homogeneous turbulent flows. Zbl 0838.76060
Debussche, A.; Dubois, T.; Temam, Roger
1995
Inertial manifolds with delay. Zbl 0822.34041
Debussche, A.; Temam, R.
1995
Stochastic Burgers’ equation. Zbl 0824.35112
Da Prato, Giuseppe; Debussche, Arnaud; Temam, Roger
1994
Convergent families of approximate inertial manifolds. Zbl 0836.35063
Debussche, A.; Temam, R.
1994
Approximation of exponential order of the attractor of a turbulent flow. Zbl 0814.76030
Debussche, A.; Dubois, T.
1994
On the discretization of a partial differential equation in the neighborhood of a periodic orbit. Zbl 0791.65071
Alouges, François; Debussche, Arnaud
1993
A convergent family of approximate inertial manifolds. Zbl 0769.34047
Debussche, A.; Temam, R.
1993
...and 6 more Documents
all top 5

### Cited by 1,580 Authors

 54 Debussche, Arnaud 40 Wang, Bixiang 35 Guo, Boling 33 Caraballo Garrido, Tomás 30 Duan, Jinqiao 30 Röckner, Michael 28 Temam, Roger Meyer 26 Da Prato, Giuseppe 26 Flandoli, Franco 26 Zhou, Shengfan 24 Langa, Jose’ Antonio 23 Gao, Hongjun 21 Hairer, Martin 21 Hong, Jialin 20 Gess, Benjamin 20 Zhao, Wenqiang 19 Li, Yangrong 19 Oh, Tadahiro 18 Real Anguas, José 18 Zhu, RongChan 17 Huang, Jianhua 17 Kloeden, Peter Eris 17 Lu, Kening 17 Romito, Marco 16 Brzeźniak, Zdzisław 16 Glatt-Holtz, Nathan E. 16 Jentzen, Arnulf 16 Marín-Rubio, Pedro 16 Miranville, Alain M. 16 Shu, Ji 15 Barbu, Viorel 15 Gu, Anhui 15 Razafimandimby, Paul André 15 Zhu, Xiang-Chan 14 Blömker, Dirk 14 Hofmanová, Martina 14 Robinson, James Cooper 13 de Bouard, Anne 13 Dong, Zhao 13 Tachim Medjo, Theodore 12 Karlsen, Kenneth Hvistendahl 12 Li, Dingshi 12 Wang, Zhaojuan 12 Yamazaki, Kazuo 11 Cui, Hongyong 11 Gubinelli, Massimiliano 11 Larsson, Stig 11 Schmalfuß, Björn 11 Weber, Hendrik 11 Yang, Desheng 11 Zhang, Rangrang 10 Anguiano, María 10 Hausenblas, Erika 10 Lisei, Hannelore 10 Shi, Lin 10 Vallet, Guy 10 Wu, Jianglun 10 You, Bo 9 Chen, Yong 9 Crauel, Hans 9 Cui, Jianbo 9 Guo, Chunxiao 9 Kovács, Mihály 9 Luo, Dejun 9 Wang, Renhai 9 Wang, Xiaohu 9 Zhou, Guoli 8 Bréhier, Charles-Edouard 8 Ferrario, Benedetta 8 Grasselli, Maurizio 8 Guo, Yanfeng 8 Högele, Michael Anton 8 Lv, Guangying 8 Maslowski, Bohdan 8 Valero, José 8 Vovelle, Julien 8 Wang, Guolian 8 Wang, Wei 8 Xin, Jie 8 Zhang, Deng 8 Zhang, Tusheng S. 7 Albeverio, Sergio A. 7 Bauzet, Caroline 7 Goldys, Beniamin 7 Goreac, Dan 7 Ju, Xuewei 7 Li, Desheng 7 Ma, Qiaozhen 7 Scarpa, Luca 7 Tang, Hao 7 Titi, Edriss Saleh 7 Wang, Xiaojie 7 Wang, Yejuan 7 Yang, Meihua 7 Zelik, Sergey V. 7 Zhang, Jian 6 Andersson, Adam 6 Bates, Peter W. 6 Bonfoh, Ahmed S. 6 Breit, Dominic ...and 1,480 more Authors
all top 5

### Cited in 268 Serials

 118 Journal of Differential Equations 76 Journal of Mathematical Analysis and Applications 65 Stochastic Processes and their Applications 61 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 49 Stochastics and Dynamics 48 Discrete and Continuous Dynamical Systems. Series B 43 Stochastic and Partial Differential Equations. Analysis and Computations 38 Stochastic Analysis and Applications 35 Journal of Mathematical Physics 31 The Annals of Probability 29 Communications in Mathematical Physics 29 Discrete and Continuous Dynamical Systems 27 Journal of Functional Analysis 25 Journal of Computational Physics 25 Applied Mathematics and Computation 23 Applied Mathematics and Optimization 22 Probability Theory and Related Fields 21 Communications on Pure and Applied Analysis 20 Journal of Statistical Physics 20 Physica D 20 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 18 Journal of Scientific Computing 18 NoDEA. Nonlinear Differential Equations and Applications 17 Journal of Dynamics and Differential Equations 17 Potential Analysis 17 Abstract and Applied Analysis 17 Nonlinear Analysis. Real World Applications 16 Applied Numerical Mathematics 15 Mathematics of Computation 14 The Annals of Applied Probability 14 Infinite Dimensional Analysis, Quantum Probability and Related Topics 14 Journal of Evolution Equations 13 Computers & Mathematics with Applications 12 ZAMP. Zeitschrift für angewandte Mathematik und Physik 12 BIT 12 Numerische Mathematik 12 SIAM Journal on Numerical Analysis 12 Transactions of the American Mathematical Society 12 Journal de Mathématiques Pures et Appliquées. Neuvième Série 12 Advances in Difference Equations 11 Computers and Fluids 11 Nonlinearity 11 SIAM Journal on Control and Optimization 10 Archive for Rational Mechanics and Analysis 10 Journal of Computational and Applied Mathematics 10 Applied Mathematics and Mechanics. (English Edition) 10 Applied Mathematics Letters 10 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 10 Journal of Difference Equations and Applications 10 Boundary Value Problems 10 Discrete and Continuous Dynamical Systems. Series S 9 Chaos, Solitons and Fractals 9 SIAM Journal on Mathematical Analysis 9 Electronic Journal of Probability 9 Acta Mathematica Sinica. English Series 9 Dynamical Systems 9 Science China. Mathematics 8 Journal of Nonlinear Science 8 SIAM Journal on Scientific Computing 8 Journal of Mathematical Fluid Mechanics 8 Stochastics 7 Applicable Analysis 7 Statistics & Probability Letters 7 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 7 Journal of Theoretical Probability 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 6 Annali di Matematica Pura ed Applicata. Serie Quarta 6 Chinese Annals of Mathematics. Series B 6 Journal of Hyperbolic Differential Equations 6 SIAM/ASA Journal on Uncertainty Quantification 6 AIMS Mathematics 5 Mathematical Methods in the Applied Sciences 5 Inventiones Mathematicae 5 Acta Mathematicae Applicatae Sinica. English Series 5 Communications in Partial Differential Equations 5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 5 Bulletin des Sciences Mathématiques 5 Mathematical Problems in Engineering 5 Journal of Inequalities and Applications 5 Communications in Nonlinear Science and Numerical Simulation 5 Frontiers of Mathematics in China 4 Computer Methods in Applied Mechanics and Engineering 4 Communications on Pure and Applied Mathematics 4 Journal of Mathematical Biology 4 Czechoslovak Mathematical Journal 4 Proceedings of the American Mathematical Society 4 RAIRO. Modélisation Mathématique et Analyse Numérique 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 4 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 4 Communications in Contemporary Mathematics 4 Foundations of Computational Mathematics 4 Milan Journal of Mathematics 4 Communications in Computational Physics 4 Journal of Applied Analysis and Computation 4 Forum of Mathematics, Sigma 4 Evolution Equations and Control Theory 4 East Asian Journal on Applied Mathematics ...and 168 more Serials
all top 5

### Cited in 45 Fields

 1,208 Partial differential equations (35-XX) 1,086 Probability theory and stochastic processes (60-XX) 481 Dynamical systems and ergodic theory (37-XX) 300 Fluid mechanics (76-XX) 275 Numerical analysis (65-XX) 102 Ordinary differential equations (34-XX) 78 Statistical mechanics, structure of matter (82-XX) 67 Systems theory; control (93-XX) 63 Operator theory (47-XX) 53 Calculus of variations and optimal control; optimization (49-XX) 51 Quantum theory (81-XX) 50 Biology and other natural sciences (92-XX) 46 Geophysics (86-XX) 25 Mechanics of deformable solids (74-XX) 19 Classical thermodynamics, heat transfer (80-XX) 17 Real functions (26-XX) 15 Integral equations (45-XX) 13 Global analysis, analysis on manifolds (58-XX) 12 Functional analysis (46-XX) 10 Statistics (62-XX) 9 Measure and integration (28-XX) 9 Computer science (68-XX) 9 Mechanics of particles and systems (70-XX) 9 Operations research, mathematical programming (90-XX) 8 Optics, electromagnetic theory (78-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Difference and functional equations (39-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Potential theory (31-XX) 4 Approximations and expansions (41-XX) 3 Differential geometry (53-XX) 3 Relativity and gravitational theory (83-XX) 3 Astronomy and astrophysics (85-XX) 2 Associative rings and algebras (16-XX) 2 Functions of a complex variable (30-XX) 2 Special functions (33-XX) 2 Integral transforms, operational calculus (44-XX) 2 Manifolds and cell complexes (57-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 General topology (54-XX)